Methods of assaying chemical or biological molecules are based, in general, on the application of protocols for blending chemical or biological reagents in liquid solution, in well-defined concentrations and in a well-defined reaction volume. By way of example, in the case of enzyme detection as used in the ELISA test method, the concentration of the enzyme product that has to be measured is inversely proportional to the volume in which the reaction takes place. Errors in measuring the volumes of the various reagents used therefore have a direct impact on the result of the measurement.
In addition, in the case of biological or chemical assays for medical diagnostics, it is advantageous, and increasingly necessary, to be able to certify, for each test result, that the biochemical protocol used to obtain this result was correctly followed. This traceability of the protocol procedure means that ways must be found for accurately measuring the volume of each of the reagents used, and for guaranteeing that they have been correctly dispensed in the reaction volume.
To meet this need to control the measurement volume a vast range of technical solutions have been developed. Manual solutions are generally based on the defined geometry of the volume drawn up or dispensed (volumetric pipettes, manual or motorized pipettes having a set or adjustable volume, syringe pipettes, multichannel pipettes). These systems generally provide a measurement volume which is reproducible, precise, on the condition that the tool is regularly calibrated, and obtained with a low throughput.
In automated systems with a higher throughput, the draw-up and the dispensing of volumes are preferably carried out by very reproducible systems, the volumes drawn up and dispensed being regularly checked by an associated measurement system. The volume drawn up or dispensed may be measured in the reservoir into which the volume is drawn up or in the receptacle into which the volume is dispensed: the contents may be weighed, or the level of the contents may be checked using an optical method or electrical contacts or impedance measurement.
These methods have a number of drawbacks: high precision for small volumes (between 10 and 100 μl) is achieved with difficulty and these methods are sensitive to effects linked to high throughputs. Mention will be made, among others, of the liquid meniscus being disturbed by the movement of the receptacle or the violence of the dispensing, the formation of bubbles or, in the case of weight measurement, the inertia of the receptacle and of the volume dispensed.
Another solution consists in determining the volume drawn up or dispensed by measuring the time-profile of the liquid flow rate in the sampling tool.
Many methods have been developed for measuring the flow rate of liquids flowing in tubes and channels of various sizes. These methods are based on various physical principles: heat transfer, mechanical, optical or electrical methods and, more precisely, magnetohydrodynamic or electrokinetic methods.
The thermal, mechanical and optical methods have the advantage of being independent of the electrical conductivity of the liquids, which may be different from one liquid to another. They have, on the other hand, the drawback of being technically complex to implement.
In addition, such systems are difficult to miniaturize. In systems for drawing up and dispensing small volumes, the liquid is generally drawn up from the bottom of a thin tube or a narrow-necked flask, and, once drawn up, is in the flared end of a cone or needle.
Mechanical, thermal or optical systems are generally too bulky to be placed directly at this location and must therefore be remote, thereby requiring an indirect measurement, via a liquid or air piston, of the volumetric flow rate at the top of the device.
Electrical methods are strongly dependent on the conductivity of the solutions, but they are the easiest to put in place and implement, especially in a miniaturized format, which makes it possible to implement them near the free end of the aspirating/dispensing device that forms the input to the sampling instrument.
Electrokinetic methods are associated with the movements of an electrolyte in a region near a solid surface. An electrical double layer is characteristic of this region.
This electrical double layer is explained in the article “Effets de la double couche électrique sur un écoulement de Poiseuille” (Electrical double layer effects in a Poiseuille flow) by C. Lattes, S. Colin, S. Geoffroy and L. Baldas, in La Houille Blanche (Hydroelectric Power), 1 (2006) pp 47-52. It may be summarized as follows.
When a conductive liquid, even a very weakly conductive liquid such as ethanol, is brought into contact with a solid sidewall such as a metal, a metal oxide, a biased semiconductor or, finally, solid sidewalls made of carbon, graphite or carbon nanotubes, the sidewall acquires an electric charge. The metal may be for example gold, platinum or stainless steel; the metal oxide may be ITO (indium tin oxide); and, the semiconductor may be silicon or diamond. Mention may also be made of solid sidewalls made of carbon, graphite or carbon nanotubes. The charge on the sidewall depends, in particular, on the ionization and therefore the pH of the solution, and on the ability to adsorb, onto the sidewall, or to dissolve, into the liquid, ions at the sidewall-liquid interface. For example, in the case of silicon in contact with water, the dissociation of molecules at the sidewall produces a negatively charged surface according to the reaction: SiOH (at the surface) +OH− SiO− (at the surface) +H2O.
This results in a local modification of the ion concentration in the solution. The region affected by this redistribution of charge in the liquid is called the electrical layer. The Stern model is used in most studies and it presents this layer as a electrical double layer (EDL) comprising:                a thin, compact layer (called the Stern layer), having a thickness xH, composed of ions adsorbed on the surface of the sidewall and aligned along a plane (called the Stern plane); and        a diffuse layer (called the Gouy-Chapmann layer) in which the ions are mobile.        
Thus, movements applied mechanically or resulting from electric fields can be observed only in the diffuse Gouy-Chapmann layer and not in the Stern layer adjacent the sidewall because convection therein is always negligible.
The charges on the surface of the sidewall are balanced by charges adsorbed in the Stern layer and by charges in the diffuse layer, thus maintaining the electroneutrality of the whole. This state is called convective-diffusive charge equilibrium (CDE) in the electrical double layer at the sidewall interface. For a given liquid/sidewall pair, it is a characteristic of the flow. The CDE depends on convection (that operates in the flow direction) and on diffusion (that operates perpendicular to the flow direction).
The distribution of ions in the solution creates an electric field the magnitude of which decreases with distance from the sidewall.
The plane separating the Stern from the Gouy-Chapmann layer is a shear plane. The electrical potential at this plane, characteristic of the CDE, is the zeta potential ζ, also called the electrochemical or electrokinetic potential.
The thickness of the electrical double layer is defined as:δ=√{square root over ((εεζkhT/2n0e2z2),)}where n0 is the initial concentration, z is the valence of the ions, e is the charge on an electron, kb is Boltzmann's constant and T is the temperature.
According to Stern, at a distance equal to three times δ the electrical potential ψ has decreased by 98% relative to its value ψ0 at the surface of the electrode. Thus δ is characteristic of the thickness of the liquid layer in which the variation in electrical potential is significant.
Depending on the properties of the liquid, the thickness δ of the electrical double layer varies from a few nanometers to about a micron.
J. Collins and A. P. Lee proposed, in their article entitled “Microfluidic flow transducer based on the measurement of electrical admittance” published in Lab on a Chip, 4 (2004) pp 7-10, a device that measured the capacitance formed between two bare electrodes placed transversely relative to the flow and between which a potential was applied from outside. The flow modifies this capacitance by affecting the thickness of the double layer.
This first device has the drawback of being dependent on the liquid the flow rate of which it is desired to measure, since the current measured is proportional to the conductivity of the liquid. Furthermore, by applying a current between the electrodes, there is a risk of hydrolyzing the solution.
Karin D. Caldwell and Marcus N. Myers proposed, in their article entitled “Flowmeter Based on Measurement of Streaming Potentials” published in Anal. Chem., 58 (1986) pp 1583-1585, a device that measured the potential between two bare electrodes placed longitudinally relative to a flow, that is to say one electrode was upstream of the other relative to the flow direction of the liquid. These electrodes were placed in a sleeve that had to be placed longitudinally, between two sections of a channel, and that had a diameter greater than that of the channel.
The potential that appears is linked to mobile electric charges being carried within the liquid from one electrode to the other. This streaming potential opposes the flow of the solution.
This second device also has the drawback of being dependent on the liquid the flow rate of which it is desired to measure, since the voltage measured is inversely proportional to the conductivity of the liquid. Furthermore, it is necessary to allocate a certain length for integration of the measurement sleeve into the channel.